to explain Gauassian elimination with examples is a big job, and 30pts is not going to attract many people to this question.

Solved

Posted on 2004-11-21

Can someone explain me (with examples) the gaussian Algorithm with Column pivot search (I'm not english, so I'm not sure if it is the right name for it).

Thanks =)

Thanks =)

7 Comments

2y + z = 1

2x + y + z = 0

3x + 3y + z = 2

0 2 1 | 1

2 1 1 | 0

3 3 1 | 2

find largest in col1 and swap row to row1

3 3 1 | 2

2 1 1 | 0

0 2 1 | 1

divide row 1 by pivot value ie 3

1 1 1/3 | 2/3

2 1 1 | 0

0 2 1 | 1

eliminate in col 1

1 1 1/3 | 2/3

0 -1 1/3 | -4/3

0 2 1 | 1

find largest in col2 diagonal and below and swap that row into row 2

1 1 1/3 | 2/3

0 2 1 | 1

0 -1 1/3 | -4/3

divide by pivot value, ie 2

1 1 1/3 | 2/3

0 1 1/2 | 1/2

0 -1 1/3 | -4/3

eliminate in col 2

1 1 1/3 | 2/3

0 1 1/2 | 1/2

0 0 5/6 | -5/6

ie

x + y + 1/3z = 2/3

y + 1/2z = 1/2

5/6z = -5/6

now back substitute

5/6z = 5/6 => z=-1

y + 1/2z = 1/2 => y = 1/2- 1/2z =1

x + y + 1/3z = 2/3 =>x = 2/3 - y -1/3z = 1-1/3-2/3 = 0

x=0 y=1 z=-1

(substituting in to orignal equations for a check shows this is correct)

Title | # Comments | Views | Activity |
---|---|---|---|

Tricky equity split scenario after house is sold | 4 | 63 | |

[week] - duration other than 7 days? | 8 | 42 | |

new car buying (price bargaining) ideas.. | 5 | 77 | |

Triangle - calculating angles | 9 | 39 |

Join the community of 500,000 technology professionals and ask your questions.

Connect with top rated Experts

**15** Experts available now in Live!